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A comprehensive study on the roles of viscosity and heat conduction in shock waves
- Qingbo Zhu, You Wu, Wenyuan Zhou, Qingchun Yang, Xu Xu
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- Journal:
- Journal of Fluid Mechanics / Volume 984 / 10 April 2024
- Published online by Cambridge University Press:
- 12 April 2024, A74
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- Article
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Shock waves are of great interest in many fields of science and engineering, but the mechanisms of their formation, maintenance and dissipation are still not well understood. While all transport processes existing in a shock wave contribute to its compression and irreversibility, they are not of equal importance. To figure out the roles of viscosity and heat conduction in shock transition, the existence of smooth shock solutions and the counter-intuitive entropy overshoot phenomenon (the specific entropy is not monotonically increasing and exhibits a peak inside the shock front) are theoretically and numerically investigated, with emphasis on the effects of viscosity and heat conduction. Instead of higher-order hydrodynamics, the Navier–Stokes formalism is employed for its stability and simplicity. Supplemented with nonlinear thermodynamically consistent constitutive relations, the Navier–Stokes equations are adequate to demonstrate the general nature of shock profiles. It is found that heat conduction cannot sustain strong shocks without the presence of viscosity, while viscosity can maintain smooth shock transition at all strengths, regardless of heat conduction. Hence, the critical role in shock compression is played by viscosity rather than heat conduction. Nevertheless, the dispensability of heat conduction would not compromise its essential role in the emergence of an entropy peak. It is the entropy flux resulting from heat conduction that neutralises the positive entropy production and thus prevents the decreasing entropy from violating the second law of thermodynamics. This mechanism of entropy overshoot has not been addressed previously in the literature and is revealed using the entropy balance equation.
3 - Atherosclerosis
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- By Gillian Cockerill, Department of Clinical Sciences, St George's Hospital Medical School, London, UK, Qingbo Xu, Department of Cardiology, King's College, University of London, UK
- Robert Fitridge, University of Adelaide, Matthew Thompson, St George's Hospital Medical School, London, UK
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- Book:
- Mechanisms of Vascular Disease
- Published by:
- The University of Adelaide Press
- Published online:
- 05 June 2012
- Print publication:
- 01 June 2011, pp 25-42
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Summary
INTRODUCTION
Atherosclerosis, the principal cause of heart attack, stroke, and peripheral vascular disease, remains a major contributor to morbidity and mortality in the Western World. Disease progression is slow, beginning in childhood and usually becoming clinically manifest in middle age or later. Although the aetiology of atherosclerosis is not fully understood, it is generally accepted that atherosclerosis is a multifactorial disease induced by the effects of various risk factors on appropriate genetic backgrounds. Many risk factors, such as hypercholesterolemia, modified lipo-proteins, hypertension, diabetes, infections and smoking have been identified in the development of atherosclerosis.
Atherosclerosis has been the focus of intense research for over 100 years. Since Anitschkow and Chalatow first reported that cholesterol can cause atherosclerosis, many investigators have intensively studied the role of blood cholesterol in the pathogenesis of atherosclerosis. Although formerly considered a bland lipid storage disease, new insights into the pathogenesis of atherosclerosis have emerged during the last decades, due to the progress of cellular and molecular approaches to the study of cell interactions in the arterial wall as well as alterations of lipid metabolism. These new insights were broadly summarized in three main theories, i.e. the ‘response to injury’, ‘oxidized low-density lipoprotein (LDL)’, and ‘inflammation’ hypotheses.
The response to injury hypothesis relies on the concept that the primary cause of atherosclerosis is an injury to the arterial endothelium induced by various factors, i.e. smoking, mechanical stress, oxidized-LDL, homocysteine, immunological events, toxins, viruses, etc.